Vol. 117 (2010) ACTA PHYSICA POLONICA A No. 4

Proceedings of the 4th Polish Symposium on Econo- and Sociophysics, Rzeszów, Poland, May 7–9, 2009

Complexity of Social Systems

C. Mesjasz∗ Cracow University of Economics, Rakowicka 27, PL-31-510 Kraków, Poland The term “complexity” used frequently as a kind of “buzzword” has gained a specific role in the language of modern social sciences and social practice. A question is arising — how can we understand complexity of social systems/social phenomena which are characterized by limited possibility of explanation, unpredictability or low reliability of prediction? The aim of the paper is to provide a partial answer to this question. A survey of characteristics of complex systems and typology of various kinds of complexity, and of their sources is presented. It is also shown that broadly defined social systems (human systems) are affected by all kinds of complexity — they are “complexities of complexities”. Using the typology of interpretations of complexity as an example, it is shown what are the limitations of transferring knowledge from physics, chemistry, information theory and biology to the studies of complexity of social systems. It is especially emphasized that mathematical models, which are treated as objective when applied in social sciences must be considered as an element of intersubjective discourse.

PACS numbers: 05.45.−a, 89.65.Ef, 89.65.−s, 89.75.−k

1. Introduction A question is thus arising — how can we understand complexity of social systems/social phenomena†. If lim- ited possibility of explanation, unpredictability or low The term “complexity” used frequently as a kind of reliability of prediction is the key feature of complexity, “buzzword” has gained a specific role in the language of what ideas drawn from complexity studies can help social modern science and social practice. At the same time sciences in better understanding of social systems? “complexity scholars”, i.e. the authors claiming to study This question is of a special significance in policy- complexity of nature and society, purposively or not, -oriented, normative sciences dealing with society — eco- directly or not, stimulate expectations of policy mak- nomics, finance, management theory, international rela- ers by attributing marketing-like titles to their works tions, security theory, peace and conflict studies, which and courses — “Hidden Order” [1], “Harnessing Complex- aim not only at description and explanation, but also at ity” [2], “Order out of Chaos” [3], “Understanding Com- providing guidance for action. plex Systems/Organizations” (repeated in various con- The need or the fashion of studying complexity of so- texts). ciety has brought about a tremendous wave of writings Recently imagination of readers curious about the in which the authors, should it be sociologists, political causes and consequences of the financial turmoil was mes- scientists, economists, mathematicians, physicists, biol- merized by such creatures as “Black Swan” [4] or mysteri- ogists, make attempts to describe, explain and, in par- ous “Dragon-Kings” running away from the power law [5], ticular, predict phenomena occurring in social life, and which are metaphorically reflecting the results of appli- recently, especially in finance. cations of complex systems models — the “power law” There are numerous writings in social sciences, eco- in particular, in studying that turmoil and in putting nomics, management and finance where authors use such in doubt traditional statistical apparatus of theory or concepts as system, stability, turbulence, adaptation, finance. self-organization, equilibrium, complexity, chaos, fractal The demand from policy makers, military planners, politics, attractors, catastrophes, emergence, etc. Char- bankers, financiers, managers and attempts to provide a acter of applications of those concepts vary, beginning response by the scholar community is nothing unusual by from mathematical models and ending with analogies and itself. A new element in the discourse between practice metaphors, with dominance of the latter two. and “complexity studies” is resulting from awareness of On the other hand, in the works rooted in broadly de- limited possibility, or even impossibility of analysis and fined systems thinking (systems approach, systems the- prediction of social phenomena. This impossibility is of- ory), complex adaptive systems theory, complexity stud- ten expressed in a declaration of fuzzily defined “com- ies, or even more ambitiously, “complexity science”, many plexity” of the subject of research.

† Social system is understood herein as human system (including ∗ e-mail: [email protected] conscious and self-conscious actors). In general sense, social sys- tems may also include other actors — animals or artificial agents.

(706) Complexity of Social Systems 707 authors discover that their concepts used as mathemati- Due to its very character — a preliminary survey and cal models or as analogies and metaphors, could help to an introduction to further research, the paper does not encapsulate various aspects of social reality. Such appli- cover the entire problem area and many issues/works cations span from social organization at the micro-level have been left for further deepened considerations. (group, company, etc.) and end at the level of broadly de- fined international relations or even global system. Some 2. Defining complex systems of the terms associated with systems thinking and/or complexity have even become a kind of “buzzwords” of 2.1. Characteristics of complexity social theory and practice, frequently used in a trivial- ized way. Numerous problems arise in defining terms associated There also exists a specific “missing link" between so- with “studies of complexity”, “complex systems studies”, cial sciences and systems thinking, and complexity stud- or the like. The author refrains from using the terms ies. On the one hand, specialists in social sciences fre- “complexity theory”, or “complexity science” although an quently refer but to very general intuitions or simpli- idea of “emerging sciences of complexity” has been al- fied interpretations of system, chaos, complexity. On ready proposed by Waldrop [9]. The challenges were even the other hand, scholars interested in applications of reflected in the article of Horgan [10] titled: “From Com- the ideas of systems and complexity to social issues ig- plexity to Perplexity”. There is not any commonly ac- nore actual knowledge in more or less established disci- cepted definition of complexity and elaboration of such a plines, such as, for example, economics, management or definition seems neither needed nor achievable. finance. Perhaps the latter discipline constitutes an ex- The first attempts to study complex entities go back ception since studies in econophysics must be based upon to the works of Weaver [11] (disorganized complexity and competence in finance theory. organized complexity), Simon [12] (the architecture of Although this exchange of ideas concerns all social sci- complexity), and Ashby [13] (the law of requisite variety). ences yet it has a special importance for normative areas In his search for explaining the meaning of complexity — economics, political science, security studies, manage- Lloyd [14] identified 31 definitions of complexity. Later ment and finance. In all security-oriented theories and this number increased to 45 [15]. In other writings nu- policies, three basic human desires are expressed. First, merous definitions and interpretations of complexity and to overcome uncertainty by enhancing predictive capabil- of its characteristics have been formulated and scruti- ities. Second, to set the rules of social behavior allowing nized — [1, 3, 9, 16–23]. to enhance the feeling of certitude, security and safety. It is obvious that a large number of definitions of com- Third, to elaborate methods to implement those rules. plexity/complex systems leads to multitude of their char- Since “complexity” is the key concept in all those con- acteristics. They are extensively described in the works siderations, it is necessary to ask a question: Is it possible referred to in the paper. to describe complexity of social systems knowing that any Assuming that no deepened discussion about defini- unequivocal definition is unfeasible? tions of systems are needed — system is an entity com- The aim of the paper is to provide at least a partial posed of elements and relations among them and inter- answer to this question. A survey of characteristics of acting with its environment from which it is separated in complex systems and typology of various kinds of com- a more or less fuzzy way, the following examples of char- plexity and of their sources is presented. It is also shown acteristics and typologies of complex systems/complexity that broadly defined social systems (human systems) are can be treated as representative ones. affected by all kinds of complexity — they are “complex- The most universal characteristics of complex systems ities of complexities”. are: large number of elements and interactions, non- Using the typology of interpretations of complexity as -linearity of characteristics depicting its behavior, hierar- an example, it is shown what are the limitations of trans- chical structure, non-decomposability, unpredictability, ferring knowledge from physics, chemistry, information self-organization. theory and biology to the studies of complexity of social Complexity can be also characterized by multitude of systems. It is especially emphasized that even mathemat- other ideas such as artificial life, autopoiesis, bifurcations, ical models, which are treated as objective when applied co-evolution, chaos and edge of chaos, emerging proper- in social sciences must be considered as an element of ties, far-from-equilibrium-states, fractals, instability, ir- intersubjective discourse. reducibility, power-law, self-organized criticality, sensi- The paper has two sources of inspiration. Firstly, it tivity to initial conditions (“butterfly effect”), sponta- refers to development of broadly defined systems think- neous self-organization, which are extensively depicted ing/systems approach, and secondly, it is built upon in a large number of writings quoted and not quoted in the conceptual framework used by Mirowski [6–8] in his this paper. works on the mutual links between development of mod- In some instances complexity studies or complexity sci- ern economic thought and physics, chemistry, biology and ence are identified solely with complex adaptive systems information theory. (CAS), which are treated as a specific case of multi-agent systems (MAS). There is no any commonly accepted in- terpretation of complex adaptive systems. Following the 708 C. Mesjasz initial concepts of CAS [1], their most representative a transcomputational capacity (beyond the Bremermann properties are as follows: non-linearity of interactions limit). (internal and external), emerging properties and simple Coming from this typology, he defined “observed ir- rules of behavior of elements, self-organization, diversity reducible complexity (OIC)” as those states of unpre- of internal structure, existence at the edge of chaos, co- dictability, which allow to classify an object in one of -evolution with environment, those three classes ([22], p. 5). Taking this typology and The above list is obviously not complete. Complex definition as a point of departure, it is proposed to distin- adaptive systems are regarded at present as an instru- guish semantically different meaning of complexity and ment of modeling of collective phenomena in all disci- identify its sources. plines of science. Due to possibility of creating elements The first class of complexity, which can be called self- of theoretically unlimited variety of behavior they are -referential complexity, includes two classes: logical com- perceived as most promising tool of modeling of broadly plexity and relational complexity. It relates to numerous defined social phenomena/social systems. forms of undecidability and interactions between observ- Methods applied in complexity studies include: agent- ing systems and in some way allows one to link objective -based modeling (otherwise known as generative com- and subjective sources of complexity [25]. puter simulation), cellular automata, catastrophe theory, Logical complexity has two interrelated components. complex adaptive systems, data mining, dynamical sys- The first one, which is in some way external to the ob- tems theory (otherwise known as chaos theory), fractal server, can be related to Gödel’s incompleteness theo- geometry, genetic algorithms, neural networking (other- rem, Post’s halting problem and Turing’s undecidabil- wise known as distributed artificial intelligence), power ity. It can be also linked to the later works concern- law, scale-free networks, self-organized criticality, syner- ing the very foundations of probability theory and of getics. mathematics in general, which have been described in In a recently proposed typology [24], complex systems the works by Kolmogorov [26] and Chaitin [27] and studies can be viewed as a result, or even a kind of em- are used under different names — descriptive complex- anation of most of the trends of broadly defined systems ity, Solomonoff–Kolmogorov complexity, Kolmogorov– thinking/systems research, cybernetics and artificial in- Chaitin complexity, stochastic complexity, algorithmic telligence. A large number of definitions and approaches entropy, or program-size complexity. to complexity puts in doubt any attempts to search for a The sense of the “objective” component of logical com- unique meaning, or a limited number of interpretations plexity can be summarized that if a formal system is of that concept. There are numerous domains of the- coherent, it is impossible to demonstrate the truth of ory and practice where this utterance has various mean- all theorems which could be built in it. Some of them ings. While it does not create problems within those would remain undecidable, i.e. not certainly true or cer- domains, it may lead to distortions in communication tainly false. It creates insurmountable limits to knowl- between them. edge which can be overcome neither in infinite time nor 2.2. Types and sources of complexity with infinite computation power [22]. The second component of logical complexity brings In order to identify the meaning of complexity, based about its subjective sources. In a radical construc- on some properties of the relationships between human tivist approach, any single cognitive (observing) system, observers, or observing systems in general, and all kinds and specifically a human being, is also affected by self- of observed systems, natural and artificial, including the -reference due to the fact that self is also thinking itself social ones, Biggiero ([22], p. 3, p. 6) treats predictabil- (and about itself) [22, 25, 28–30]. Therefore undecid- ity of behavior of an entity as the fundamental crite- ability affects also the observer and the very process of rion for distinguishing various kinds of complexity. As a observation. foundation he proposes an interpretation of complexity as a property of objects which are neither deterministi- The second kind of self-referential complexity, derives cally nor stochastically predictable. “Complexity refers from limitations of interactions and communication be- to objects which are predictable only in a short run and tween observers, and obviously, observers/participants that can be faced only with heuristic and not optimizing in social systems composed of conscious elements. It strategies” ([22], p. 6]). is the core of concept of “second-order cybernetics” [25] He proposes three classes (groups) of complexity‡: and “soft” systems thinking [31]. Leaving apart too fre- (a) objects not deterministically or stochastically pre- quently abused in social sciences the Heisenberg princi- dictable at all, (b) objects predictable only with infinite ple, it may be stated that interactions between observers/ computational capacity, (c) objects predictable only with participants and the system under observation as well as communication between observers/participants is never indifferent and is always exposed to distortions. Next class of complexity and its sources, which can be ‡ The term “class” is used in the paper in a non-rigorous way which called gnosiological complexity, includes two subclasses: is demanded in classification theory. It is rather a grouping of fundamental gnosiological complexity and semiotic com- types. plexity. Complexity of Social Systems 709

Fundamental gnosiological complexity is associated and computational intractability. Logical intractability with the infinite types of distinctions that an observer to a large extent overlaps with logical complexity, es- can hypothetically make regarding himself/herself and in pecially in the concepts developed in the second half of his/her own environment [25, 29, 32–35]. In this case the the 20th century by Solomonoff, Kolmogoroff [26] and definition of information by Bateson ([32], p. 459) “dif- Chaitin [27]. ference which makes a difference" is the point of depar- Computational complexity occurs when it is impossi- ture: The observer is never able to identify all differences ble to end computing either because of infinite or “prac- (all information) characterizing reality (environment and tically excessive” resources needed for computation (time himself/herself). It may be even disputable to what ex- or computing power). Computational (algorithmic) com- tent the observer in the process of construction invents plexity theory concerns intractability in measuring com- or discovers reality. In the discussion going down to the putational resources in terms of program execution time. biological level Maturana and Varela [28] argue that even In simplest way it can be described as follows. Depend- neurophysiological signals are not objective, because the ing on the type of solvability by different Turing machines external environment reaches the brain mixed with sig- the polynomial time algorithms, called NP class, can be nals and noises coming from inside of the observer. divided into three classes. First, class P concerns al- Semiotic complexity derives from the infinite possible gorithms solvable with a deterministic Turing machine. meanings which can be assigned by an observer to any Second, class NP-complete, concerns algorithms solvable perceived distinction/information [30, 36, 37]. It refers only with a nondeterministic Turing machine. Third, to the irreducible ambiguity of events, facts and infor- class NP-intermediate, also deals with algorithms solv- mation. Assigning meaning (sense-making) depends on able only with a nondeterministic Turing machine. the subjectivity (history and structure) of the observer. Both NP problems solvable only with a nondeterminis- Subjectivity is also strongly dependent on language and tic Turing machine are considered as intractable with an culture. The same fact can be interpreted differently by exception of small inputs. Problems belonging to class P different actors. It not only affects the understanding are treated as tractable, but with a very high limits to in- but also influences the communication, as it was already put size. Due to the height of the limits they are regarded observed for relational complexity. as already intractable [42]. Computational complexity is The third class of complexity is derived from the in- a subject of intensive studies and the above explanation finite developments a nonlinear system can perform. It is an introduction to more advanced considerations [43]. can be called chaotic and non-equilibrium complexity and The above typology can be summarized with an ap- was initially assigned by Biggiero [22] to the same class proach taken from information theory. According to the as fundamental gnosiological and semiotic complexity. It rudimentary interpretation, information can be described seems, however, that due to its specificity this type of with quantitative (syntactical) and qualitative (seman- complexity should be considered as a separate type yet tic) aspects [44]. This division is equivalent to the pairs: linked to the second class of complexity. objective vs. subjective, or independent of observer and This type of complexity covers a vast area of nonlinear observer-dependent, and independent of meaning and dynamic systems including such ideas as singularity the- meaning dependent. Computational, chaotic ad logical ory, bifurcation theory, catastrophe theory and fractals complexity and its sources may be assigned to the first geometry. class while gnosiological, semiotic and relational com- Chaos emerges when a dynamic system is highly sensi- plexity and its sources are associated with meaning and tive to initial conditions or when it has numerous bifurca- natural languages. tions or singularities. In consequence, dynamic systems Two conclusions important in studying any complex become unpredictable since many different trajectories systems, and social systems in particular can be drawn. may be followed and many different fixed points (attrac- Firstly, in all discussions on complexity of social sys- tors) may emerge. tems composed of conscious elements the role of observer- According to [38] and [22], chaos, as well as dissipa- -participant must be always taken into account, even tive structures [3] and complex adaptive systems (CAS) when studies concern objectively defined complexity. [1, 9, 17], share a common property of ability of self- This postulate does not necessary mean acceptance of -organizing. Self-organizational complexity is associated radical constructivism in which observer invents reality. with unexpected appearance of ordered systems from a It only should be remembered when quantitative model- disordered aggregation of elements, e.g. self-organized ing of social systems is conducted that any of the models criticality [18], synergetics [21]. Although common in is absolutely objective. physics and chemistry, self-organization is regarded as a Second, human systems are characterized by the pres- specific feature of biological phenomena [17] and social ence of all sources and types of complexity [22]. It may phenomena [30, 38–40]. Various applications of power be then summarized that in a universal sense all many law [4, 5, 41] as well as scale-free networks [23] can also collective phenomena may be complex, including for ex- be added to this class of complexity and its sources. ample animal or artificial social systems but human sys- The fourth class of complexity is called computational tems made of conscious elements are the “complexities of complexity. It can be identified with logical intractability complexities”. 710 C. Mesjasz

of processes of production (transformation and destruc- tion) of components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in space in which they (the components) exist by speci- fying the topological domain of its realization as such a network” ([28], p. 78). The space defined by an autopoietic system is self- -contained and cannot be described by using dimensions that define another space. When we refer to our inter- Fig. 1. Types of complexity and its sources. Source: actions with a concrete autopoietic system, however, we own research and after [22]. project this system on the space of our manipulations and make a description of this projection ([28], p. 89). The most representative example of an autopoietic sys- 2.3. “Hard” and “soft” complexity tem is the biological cell, which being based on an exter- The above typologies can be supplemented with an- nal flow of molecules and energy, produce the compo- other division relevant to social sciences methodology. nents which, in turn, continue to maintain the organized This division is also a summary of different streams of bounded structure that gives rise to these components. systems thinking/complex systems studies. The first An autopoietic system is autonomous and operationally stream developed only with the use of mathematical closed, in the sense that there are sufficient processes modeling can be called “hard” complexity research as an within it to maintain the whole. analogy with “hard” systems thinking§. The “soft” com- An autopoietic system stands in opposition to an al- plexity research, also coined per analogy with “soft” sys- lopoietic system (externally created). Allopoietic is the tems thinking [31], includes qualitative concepts of com- process whereby an organization produces something plexity elaborated in other areas — cybernetics and sys- other than the organization itself, e.g. an assembly line. tems thinking, social sciences and in psychology. It is It is worthwhile to mention that Maturana and Varela necessary to stress that soft complexity initially had two drew inspiration from the concept of distinction devel- domains — purely verbal considerations on complexity, oped by Spencer–Brown [46]. and applications of the ideas from “hard” complexity in Autopoiesis refers also to the self-reference and the role qualitative considerations. At present, under the impact of observer. It is reflected in the assertion: “everything of “hard” complexity only one stream of soft complexity said is said by an observer” ([28], p. xix). Due to such studies exists [24]. a self-referential approach the concept of autopoiesis was Subjectivity/qualitative methods are the main aspect criticized as a form of solipsistic methodology and radical of complexity in the “soft” approach. It is just a con- constructivism. sequence of the fact that complexity is not an intrinsic The concept of autopoiesis was used by Luhmann to property of an object but rather depends on the observer. elaborate an indigenous theory of social systems, which In social sciences, and particularly in sociology, special has become one of most popular universal social theories. attention is given to the concepts of complexity of social He defines social system of conscious units as autopoietic systems proposed by Luhmann. First of all, as one of system of meaningful communication. Autopoiesis refers a few authors, he made an attempt to elaborate a com- not to the tangible attributes of systems but to commu- prehensive definition of a social system based solely on nication [30, 40]. communication and on the concept of autopoiesis (self- In a preliminary and simplified interpretation of intri- -creation) of biological systems. Autopoiesis means “auto cate Luhmann’s ideas, social systems operate at the level (self)-creation" (from the Greek: auto — αυτo´ for self- of a re-entry of their form into their form — concept and poiesis — πo´ιησις for creation or production), and taken directly from biological autopoiesis [28] and indi- expresses a fundamental dialectic between structure and rectly from [46]. It also means that description of the function. The concept of autopoiesis was introduced system is a part of the system. Since they use their own by Chilean biologists Maturana and Varela in the early output as input they cannot compute their own states 1970s. It was originally presented as a system descrip- but they are “autopoietic” systems, and that means that tion that was designed to define and explain the nature they are their own product. In this interpretation, social of living systems. system are thus self-reflexive and self-referential. According to its authors, “An autopoietic machine is The theories of social systems proposed by Luhmann a machine organized (defined as a unity) as a network are broadly discussed in social theory, especially in Eu- rope. When recalling Luhmann, it is necessary to real- ize the controversy about the laws of form elaborated by Spencer Brown [46] and to know that even the co-founder § The term soft complexity science was also used in [45]. of biological autopoiesis, Maturana criticized the use by Complexity of Social Systems 711

Luhmann of that idea in studying social systems ([47], server’s description of another observer’s descriptions of p. 78). complexity, or it is the result of a complex observer’s The Luhmann concept of “soft” complexity is likely its description of its own complexity [52]. most influential interpretations in contemporary social theory. According to this concept, a complex system is 3. Complexity and social systems: one in which there are more possibilities than can be ac- Mathematical models, analogies and metaphors tualized. Complexity of operations means that the num- 3.1. Reflexivity and self-reflexivity of social systems ber of possible relations becomes too large with respect to Application of the concept of complexity with its mul- the capacity of elements to establish relations. It means titude of interpretations in social sciences is becoming that complexity enforces selection. The other concept of even more difficult due to another similar obstacle — complexity is defined as a problem of observation. Now, multitude of meanings of social systems. Even if the hi- if a system has to select its relations itself, it is difficult to erarchy of social systems viewed from a global level to a foresee what relations it will select, for even if a particu- group scale is left apart, it is not possible to comprehend lar selection is known, it is not possible to deduce which all meanings of social systems. The basic assumption is selections would be made ([30], p. 81). that social systems are mental constructs of the observers The idea of complexity of Luhmann is also applied in (participants) as interpretations of behavior of their com- defining risk in social systems. The large amount of el- ponents and of the entities. ements in a given system means that not all elements The most important distinction in defining social sys- can relate to all other elements. Complexity means the tems lies thus in the role of participant-observer. If need for selectivity, and the need for selectivity means she/he remains outside the system and is not able to contingency, and contingency means risk [48]. interfere into its behavior, then a physicalist approach Complexity of social system developed by Luhmann can be applied, obviously without possibility to refer to is strongly linked to self-reference since reduction of quantum mechanics. Such an approach belongs to the complexity is also a property of the system’s own self- tradition of the “first order cybernetics” or the “hard” -observation, because no system can possess total self- systems thinking. If the participant/observer is able to -insight. This phenomenon is representative for episte- exert an impact on the system, then consequences of re- mology of modern social sciences, where observation and flexivity and self-reflexivity must be taken into account. self-observation, reflexivity and self-reflexivity, and sub- Under such circumstances the “second order cybernetics” sequently, self-reference an recursion are playing a grow- or the “soft” systems thinking are the basic methods of ing role. According to this interpretation, social systems research [25, 31]. are becoming self-observing, self-reflexive entities trying Complexity of social systems is more difficult to com- to solve arising problems through the processes of adap- prehend, since it is always a result of an intersubjective tation (learning). discourse. The “hard” approach allows us for more pre- A deeper look into subjective aspects of complexity cisely defined tangible attributes of the system described leads to the conclusion that any cognitive system must in- by measurable with “strong” ratio scale tangible char- clude at least a partial projection of its environment and acteristics. The “soft” approach makes the description of itself onto itself. A definition of complexity referring to much difficult since intersubjectivity depends on transfer that idea was proposed by Rosen, who also elaborated the of imprecise meanings in the discourse. In both cases it is concept of anticipatory system, i.e. a system containing a necessary to consider limitations stemming from reifica- predictive model of itself and/or its environment, which tion of subjective/intersubjective categories. It may thus allows it to change state at an instant in accord with the be concluded that if studies concentrate upon “tangible”, model’s predictions pertaining to a latter instant ([49], measurable attributes of social systems, then “hard” com- p. 341). According to Rosen, a system is simple if all its plexity methods, mainly mathematical models, includ- models are simulable which is approximately equivalent ing simulations, can be applied. Otherwise, the discus- to Turing-computability. A system that is not simple, sion must also include reflexive ideas taken from “soft” and that accordingly must have a nonsimulable model, is complexity studies. Therefore a mixed approach is nec- complex ([50], p. 392). essary — mathematical modeling and/or analogies and ¶ The concepts of Rosen’s anticipatory systems, has been metaphors . supplemented by the ideas of incursion (inclusive or im- There is a specific factor allowing to distinguish tra- plicit recursion) and hyperincursion (incursion with mul- ditionally defined systems thinking from complexity re- tiple solutions) developed by Dubois [51]. search, at least until the mid-1980s. While systems think- ing sought for holistic ideas and universal patterns in all Using the concept of Luhmann’s complexity, Qvortrup has put before the concept of hypercomplexity. He linked Simon’s “bounded rationality” as a limitation to choice (selection) with the complexity resulting from impossibil- ¶ The terms analogies and metaphors are applied in the paper in a ity to make that selection. Hypercomplexity is complex- simplified sense. There are also other linguistic concepts, which ity inscribed in complexity, e.g. second-order complexity. should be applied in more advanced considerations on modeling As an example, hypercomplexity is the result of one ob- and problem solving [53]. 712 C. Mesjasz kinds of systems, complexity research defined its goals in mathematics, high precision measurement made across a more specific manner. A common theoretical frame- various disciplines and confirming “universality” of com- work, the vision of underlying unity illuminating nature plexity properties, and mathematical studies embodying and humankind is viewed as an epistemological founda- new analytical models, theorems and results. tion of complexity studies [9]. This claim for unity results Models, analogies, and metaphors deriving from sys- from an assumption, that there are simple sets of math- tems thinking and complexity studies are gaining a spe- ematical rules that when followed by a computer give cial significance in social sciences. For mathematical rise to extremely complicated, or rather complex, pat- models it is quite obvious that they are associated with terns. The world also contains many extremely compli- “objective” research. Analogies and metaphors taken cated patterns. Thus, in consequence it can be concluded from complex systems studies are related to ideas drawn that simple rules underlie many extremely complicated from “rational" science. They are treated as “scientific" phenomena in the world. With the help of powerful com- and may provide additional political influence in the dis- puters, scientists can root those rules out. Subsequently, course resulting from “sound" normative (precisely pre- at least some rules of complex systems could be unveiled. scriptive), legitimacy in any policy-oriented debate. Although such an approach was criticized, as based In applications of models, analogies and metaphors in on a seductive syllogism [10, 45], it appears that it still social sciences the following approaches can be identified: exists explicitly or implicitly in numerous works in the descriptive, explanatory, predictive, anticipatory, norma- hard complexity research. tive, prescriptive, retrospective, retrodictive (backcast- There exists another, often omitted, barrier in defin- ing), control and regulation. ing tangible attributes of social systems. In some in- Bell et al. [55] have proposed to discern between the stances measurable characteristics are easily identifiable, normative approach resulting from mathematical models, e.g. physical aspects or financial measures expressed di- predominantly game models, and prescriptive approach rectly in monetary units. In some cases an intangible reflecting recommendations resulting from decision anal- category is reified as to make it measurable. The discus- ysis, including also qualitative aspects. sion on “knowledge management” or on “knowledge based Following the distinction from traditional cybernetics, economy” provides best examples. Operationalization of control and regulation approach can be also proposed. the concept of knowledge not only in economics but also In management this approach is expressed in a way the in other social sciences is usually based upon a twofold dominant analogy or metaphor influences control of a approach. On the one hand, several “tangible” attributes system, i.e. they differ for mechanistic, evolutionary or of social systems are treated as more or less representa- learning system [56, 57]. Limitations of prediction of be- tive for the state of knowledge, e.g. number of patents, havior, design and control of complex systems impose income for innovation. On the other, attempts are made also other ways of managing complex systems. Axelrod to make some unquantifiable characteristics measurable and Cohen ([2], p. xvi) proposed to “harness” complexity at least with the cardinal scale in order to use them in of social systems: “. . . to convey a perspective that is not rating and scoring methods [54]. explanatory but active — seeking to improve but without Operationalization of intangible attributes of social being able fully to control”. system always creates a trap of reification. In conse- Complexity associated with non-linear dynamics adds quence, even mathematically elegant models may have some new elements to our knowledge of social dynamics. a limited validity since they result from false or at least We do not only become aware that social systems are dubious assumptions. uncontrollable, but even desirability of such control is already put in doubt. Self-organization is regarded as a 3.2. Linguistic approach to complexity of social systems desired pattern of dynamics in economics and politics. All the above barriers of interpretations of social sys- It was already reflected in the interests of Hayek [58] tems complexity can be also explained with a linguis- in complexity of social systems as an argument against tic approach. Systems thinking/complex systems stud- centrally planned economy. ies, or whatever it may be called, can be used in social Another lesson of non-linear dynamics and complex sciences as sources of analogies, metaphors and mathe- systems teaches us is that social changes, or in a broader matical models. According to this distinction, the term sense, evolution, are produced by both deterministic his- “(formal) models" is used only for mathematical struc- torical factors and chance events that may push social tures. phenomena to new patterns of behavior. Thanks to bet- Using another approach, our questions refer to three ter understanding the confluence of chance and determin- Wittgenstein’s [35] “language games" including meaning ism in social systems we may better learn what kind of of three utterances: (1) the meaning of social systems, actions we have to undertake, or even perhaps, what kind (2) the meaning of complexity and (3) the meaning of of norms we have to apply. ideas in which the concepts of social systems and the It must be also reminded that analogies and metaphors concept of complexity are together applied. of rather loosely interpreted non-linearity, chaos, com- Mathematical models can be applied in three areas plexity, self-organization, etc. in many instances have of complexity studies: computing-based experimental become the backbone of the post-modernist (post- Complexity of Social Systems 713

-structuralist) new science. Reaffirmation of limited pre- Second, along with the differentiation, pluralism and dictability has become an epistemological foundation of multipolarity associated with the democratisation and the discourse-based science. Numerous examples can be expansion of the market economy along with their limited quoted but as an illustration it is worthwhile to recall effectiveness, e.g. the recent turmoil on financial mar- synthesis of post-modernist ideas of Braudel and Prio- kets, more attention is given to concepts drawn from gogine’s concepts on far-from-equilibrium states made by complex systems studies. However, stress must be put Wallerstein ([59], p. 160–169) in modeling social systems, not only on the “objective" soundness and mathematical although solely at a metaphorical level. elegance of these concepts. Instead, they should be seen The above epistemological links between complexity as analogies and metaphors reflecting observer-related, research and social sciences are predominantly associated emotionally-laden and normative understandings of the with the “hard” complexity. The input to this area ex- world, which not always can be operationalized. Thus in erted by the “soft” complexity research is equally signifi- studies which intend to deal with the old and new systems cant. Reflexive complexity of society has become one of thinking-related terms: autopoiesis, chaos, complexity, the foundations of post-modern social theory [30]. equilibrium, fluctuation, homeostasis, non-equilibrium, Unfortunately, various abuses and misuses may occur, self-organisation, stability, synergy, turbulence, ultrasta- when analogies and metaphors drawn from the “hard” bility, etc., it is necessary to concentrate on the semantic complexity research, and to a lesser extent from the foundations before any applications and operationaliza- “soft” complexity research are treated too carelessly even tions in studies of social systems. by eminent social theoreticians of post-modernism/post- It must be also remembered that contrary to physics, -structuralism. Several examples of such abuses are mir- mathematical modelling in social sciences, including ob- rored in the so-called “Sokal Hoax” and other examples viously complex systems, is rather rarely based upon ax- widely described by the originator of that hoax [60]. iomatic approach, perhaps with an exception of math- Summarizing the above considerations, it may be con- ematical (theoretical) economics. In other cases an ap- cluded that applications of complex systems analogies proach based upon operationalization is applied. But in and metaphors in social sciences expose two basic weak- such case the process of building operationalizable defi- nesses. First, in most of their applications it has been nitions begins from “central metaphor” or “stylized fact”, omitted that they can be predominantly used solely as a qualitative idea which is later developed with the use descriptive and explanative instruments. Application of of formal models, e.g. distribution, risk [53]. In such case those analogies and metaphors for prediction and norms- the selection of the model is subjective in all possible -setting is always limited by their reification. It brought ways — self-reflexive and self referential (from the point about double consequences. In theoretical research many of view of the modeller). futile efforts were made to make them more “scientific", As the final example of subjectivity of mathemati- “objective" and “analytical". Practice, in turn, has been cal models applied in studying social systems a dispute enriched with “objective" terms with various hidden nor- between authors of models applied in finances can be mative loading, e.g. “stability", “equilibrium”. Some of recalled. these problems could be avoided if the following phe- The divide in the dispute between forecasting in fi- nomenon were taken into account. It can be ironically nances based on classical econometric models, and mod- called “The Law of Metaphorical Infinity of Social Sys- els based on broadly defined complexity methods, gained tems": additional momentum in 2007–2008. The divide was Any theory and/or model elaborated in physics, chem- made popular by the already mentioned “Black Swan” istry, biology, automatic control theory, etc., in order to [4] although other more or less known works, e.g. [61] study collective phenomena (“systems thinking", “com- dealt with those issues well before the crisis. plexity studies”), can be applied as a source of analogies The most extreme position in that dispute has been and metaphors in various attempts aiming at descrip- recently taken by Farmer and Foley [62], who exposed tion, explanation (sometimes even prediction and pre- validity of agent-based modeling (complex adaptive sys- scription), of phenomena taking place in social systems, tems) in finance as reflecting nonlinearity and non- beginning from small groups, and ending with the world -equilibrium states, although at the same time admitting system. that those models are still at a preliminary stage of de- The Law can be supplemented with an observation velopment. that large-scale social systems seem particularly tempt- ing for such efforts. It is easy to compare a society to They add that there is no any sufficiently developed a machine or biological system. It will be much more analytical methods in financial policy at the state level. difficult to do the same with a small group or family. Two quotations seem representative for their position. The meaning of the term “society” is much broader and “This is hard for most non-economists to believe. Aren’t more distant from our everyday experiences. In the case people on Wall Street using fancy mathematical models? of a smaller group we can easier identify the humans as Yes, but for a completely different purpose: modeling the elements of the system. potential profit and risk of individual trades. There is no attempt to assemble the pieces and understand the be- havior of the whole economic system” ([62], p. 685). “The 714 C. Mesjasz policy predictions of the models that are in use aren’t [14] S. 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